QA – Placement Quizzes | Progressions | Question 10

A tennis ball is initially dropped from a building of height 180 m. After striking the ground, it rebounds (3/5)^th of the height from which it has fallen. 

Calculate the total distance that the ball traveled before it comes to rest.

(A)

540 m

(B)

600 m

(C)

900 m

(D)

None of the above

Answer: (D)

Explanation:

The total distance traveled by the ball is the sum of two infinite series: a. Series 1: the distance traveled by the ball when it\’s falling down b. Series 2: the distance traveled by the ball when it\’s bouncing up S1 = a1 / (1 – r1) and S2 = a2 / (1 – r2) S1 = 180 / (1 – 3/5) and S2 = (180 * 3/5) / (1 – 3/5) S1 = 180 / (2/5) and S2 = 108 / (2/5) S1 = 180 * 5/2 and S2 = 108 * 5/2 S1 = 450 and S2 = 270 Therefore, S = S1+S2 = 720 m.

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